The \(\gamma ^5\)  is a parity operator defined by \(\gamma ^5 = i \gamma ^0 \gamma ^1 \gamma ^2 \gamma ^3 \) , which is the only operator that commutes with all other \(\gamma ^\mu \)  matrices [1]}. The spin operator is constructed by the \(\gamma ^5\)  matrix by, in the Dirac representation [1]},
\(S^i = \frac{1}{2} \gamma ^5 \gamma ^0 \gamma ^i\) 
